System and method for determining coordinates on three-dimensional space using beam phase interference

ABSTRACT

Disclosed are a system and a method for determining coordinates of a three-dimensional measurer probe using a beam phase interference method. Two optical fibers are mounted inside the probe, and detecting means obtains an interference pattern generated by beam emitted from a point beam source mounted at ends of the optical fibers. After that, wave front of the interference pattern is measured and a location of the point beam source is determined through a nonlinear optimization from the wave front, and thereby the coordinates of the three-dimensional measurer probe are set. Because the two optical fibers of the inside of the probe to be measured are located in close vicinity to the three-dimensional object, the present measuring system and method can reduce a measurement error, make a structure of the system simple, and thereby reduce a manufacturing cost.

TECHNICAL FIELD

The present invention relates to a system and a method for determiningcoordinates of a three-dimensional measurer probe using a beam phaseinterference method. Specifically, the invention relates to a system anda method for determining coordinates of a three-dimensional measurerprobe in such a manner that two optical fibers are mounted inside theprobe, a detector obtains an interference pattern generated by beamemitted from a point beam source set at ends of the optical fibers, wavefront of the interference pattern is measured using a phase shiftalgorithm and a location of the point beam source is determined througha nonlinear optimization from the wave front, thereby determining thecoordinates of the three-dimensional measurer probe.

Because the two optical fibers set inside the probe to be measured arelocated in close vicinity to the three-dimensional object, the measuringsystem and method of the present invention can reduce a measurementerror, make a structure of the system simple, and thereby reduce amanufacturing cost.

BACKGROUND ART

FIG. 1 illustrates a system for determining three-dimensionalcoordinates using the principle of a laser interferometer. The principleis that laser beams generated from an x-axis laser interferometer 1 a, ay-axis laser interferometer 1 b and a z-axis laser interferometer 1 care inputted into a probe 3 a and interference patterns reflected bycorner mirrors 2 a, 2 b and 2 c of the probe are detected to set thethree-dimensional coordinates. In this system, the operating range ofthe probe 3 a increases when the volume of an object to be measured islarge. In the above-described procedure, the laser interferometers 1 a,1 b and 1 c are failed to target the ranges of the corner mirrors of theprobe so that the coordinate values cannot be measured. In addition, thelaser interferometers must move together with the probe as the probemoves and they are costly apparatuses. Thus, a three-dimensionalmeasurer employing the principle of the laser interferometer becomesexpensive.

To overcome the aforementioned shortcoming, another system using a laserinterferometer (shown in FIG. 1A) is constructed in a manner that x-axisand y-axis reflecting mirrors 2 x and 2 y reflect interference patternsand z-axis measures a laser interferometer apparatus using the laserinterferometer. However, this system should use two laserinterferometers and employ reflecting mirrors 2 x and 2 y, which areperfectly horizontal. Accordingly, the system becomes expensive and thesizes of the reflecting mirrors must be increased when the movementrange of the probe is extended.

FIGS. 2 and 2A illustrate laser interferometers that compensate for theshortcomings of the systems of FIGS. 1 and 1A. Laser interferometers 1e, 1 f, 1 g and 1 h are located irrespective of directions and aninterference pattern reflected by a corner mirror 2 d set at one side ofa probe is detected to measure three-dimensional coordinates. Thissystem includes a controller 91 for setting a position of the probe anda computer 90 for detecting the interference pattern to measure thethree-dimensional coordinates. This system is also expensive because ituses four laser interferometers. In addition, the laser interferometersshould rotate when the probe is moved.

DISCLOSURE OF INVENTION

An object of the present invention is to provide a new method and systemfor determining coordinates of a three-dimensional measurer probe.

To accomplish the object of the invention, there are proposed a methodand a system for determining coordinates of a three-dimensional probe byplacing two optical fibers inside the three-dimensional probe,generating an interference pattern using the optical fibers as a pointbeam source, and analyzing the interference pattern, thereby determiningcoordinates of the point beam source in the three-dimensional space.

The present invention analyzes the interference pattern in such a mannerthat wave front of the interference pattern is measured using a knownphase shift algorithm and then a location of the point beam source isdetermined through a nonlinear optimization from the wave front.

As described above, the optical fibers are simply mounted inside theprobe to easily construct the probe apparatus. Accordingly, the opticalfibers can be located in close vicinity to an object to be measuredthrough the simple structure so as to reduce a measurement error whiledecreasing a manufacturing cost.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the principle of a conventional laser interferometermodule for measuring coordinates;

FIG. 1A illustrates the principle of another conventional laserinterferometer module for measuring coordinates;

FIG. 2 illustrates the principle of an improved laser interferometermodule for measuring coordinates;

FIG. 2A illustrates a three-dimensional coordinate measuring machine;

FIG. 3 illustrates an embodiment of a three-dimensional measuring systemaccording to the present invention;

FIG. 4 is a cross-sectional view illustrating the junction of a probeand optical fibers in the system of the present invention;

FIG. 4A is a cross-sectional view illustrating another form of thejunction of the probe and the optical fibers in the system of thepresent invention;

FIG. 5 illustrates a CCD camera and optical fibers in three-dimensionalcoordinates;

FIG. 6 illustrates an embodiment of the system of the invention in whichthe number of CCD cameras is increased;

FIG. 7 illustrates another embodiment of the system of the inventionusing pin-holes;

FIG. 8 illustrates another embodiment of the system of the invention,suitable for a narrow space; and

FIG. 9 is a flow chart illustrating a step of applying voltage to PZTaccording to the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

The present invention includes a probe in which two optical fibers foremitting beams are set, a detector for detecting an interference patterngenerated by the beams emitted from the optical fibers, and acontrol/analysis unit for analyzing the interference pattern obtained bythe detector. Beams, obtained in such a manner that a fiber couplersplits a beam emitted from a single light source, are transmittedthrough different optical fibers to the two optical fibers set in theprobe. One of the two optical fibers is united with a cylindrical PZT,being wound round the PZT, in order to control an optical path. The PZTis connected to the control/analysis unit to control a single opticalpath.

Preferred embodiments of the present invention are explained below withreference to attached drawings. FIG. 3 roughly illustrates the systemaccording to the present invention.

A beam emitted from a light source 10 is inputted into a single-modefiber 30 through a lens 20 of good performance. The incident beam issplit into two beams by a fiber coupler 40 and transmitted through twodifferent optical fibers 50 and 60 to be inputted into a probe 80(referring FIG. 4). The two optical fibers 50 and 60 have the samelength and one of them is wound round a PZT 70 several times and unitedwith the probe 80 so as to change an optical path. The PZT 70 expandswhen voltage is applied thereto. Thus, when the PZT 70 accepts voltagefrom a signal sent from a computer 90, it is expended and thus theoptical fiber wound round it also lengthens, thereby changing theoptical path.

There is explained below a procedure of acquiring coordinates of a pointbeam source by obtaining the interference pattern from the light sourceand analyzing it.

When a beam is generated from the light source 10, the beam is inputtedinto the single-mode optical fiber 30 and then split by the opticalfiber coupler 40. The split beams are respectively transmitted throughthe optical fibers 50 and 60 to the ends of them being inserted into theprobe, generating spherical waves. The optical fiber wound round the PZTlengthens as the volume of the PZT expands so that the two opticalfibers 50 and 60 respectively generate spherical waves having differentphases. These spherical waves having different phases respectivelygenerate interference patterns having different initial phases. An imagecapturing unit captures the interference patterns and calculates theircurvatures using a known phase shift algorithm. A CCD camera is usuallyused as the image capturing unit and a two-dimensional line camera and athree-dimensional area camera are also used. The camera converts acaptured image value into a digital value by pixels. The curvature ofeach interference pattern can be represented by one central point. Ifthe positions of the optical filters in the probe are not changed asdescribed above, the curvatures of the interference patterns are notvaried and the central points representative of the curvatures are fixedto specific positions in the three-dimensional space. Accordingly, themovement of the probe can be determined by setting the traces of thecentral points of the interference patterns because the trace of theprobe's movement in the three-dimensional space is identical to thetraces of the central points of the interference patterns.

An object 400 to be measured is placed under the three-dimensionalmeasurer probe and the image capturing unit (CCD camera 100 was used inthe present invention) is located in front of the ends of the opticalfibers set inside the probe. It is preferable that the CCD camera 100 isplaced in front of the spherical wave 61 generated by the optical fiber60 and the spherical wave 51 generated by the other optical fiber 50.The object 400 to be measured and the CCD camera must be fixed.

To use the known phase shift algorithm, several interference patternshaving different initial phases are required. This can be accomplishedby controlling voltage applied to the PZT 70 through thecontrol/analysis unit so as to change the optical path of one opticalfiber. Generally, the control/analysis unit may include a generalcomputer, an industrial computer specially manufactured for industrialuses, a central control unit and so on. The procedure of changing theoptical path using the PZT and thereby obtaining interference patternsto calculate the curvatures of the interference patterns is well knownin the art. Thus, detailed explanation about the procedure is omitted inthe present invention.

A contact signal generated when a probing needle 81 (referring FIG. 4)set at the bottom of the probe 80 comes into contact with the object 400to be measured is transmitted to the control/analysis unit, and theimage capturing unit obtains several interference patterns havingdifferent initial phases on the basis of the contact signal. Though theprobing needle 81 described in this embodiment is of contact type, anon-contact type probe can be also employed if an auto-focusing deviceis introduced in the system. Furthermore, the probing needle can beeasily modified on the technical level of those skilled in the art.

FIG. 4 is a cross-sectional view illustrating the junction of theoptical fibers and the probe, and FIG. 4A is a cross-sectional viewillustrating another form of the junction of the optical fibers and theprobe. Covering 62 of a part of the end of each of the optical fibers 50and 60 is stripped off and cut with the end of each optical fiber andone side of the probe according with each other. A portion of the probeinto which the optical fibers are inserted is sealed so that the opticalfibers cannot come out. A measurement error can be reduced when theprobe and the object to be measured directly come into contact with eachother. However, the direct contact is unsuitable when the object issmall. Thus, the contact of the probe and the object is made using theprobing needle 81. The probe may come into contact with the objectthrough the aforementioned non-contact type probe and the contact methodcan be varied on the technical level of those skilled in the art. FIG.4A illustrates another form of the junction of the probe and the opticalfibers 50 and 60. When the junction of the probe and the optical fibersis made with the ends of the optical fibers being narrowed, sphericalwaves generated at the ends of the optical fibers have curvatures largerthan those of the spherical waves generated in the structure of FIG. 4.Accordingly, at least two image capturing units (here, CCD camera) areset to measure the curvatures and central points obtained from thecurvatures are averaged to determine a central point, resulting in moreaccurate measurement.

FIG. 5 represents the positions of the CCD camera used as the imagecapturing unit and the optical fibers 50 and 60 in three-dimensionalcoordinates.

In case where an orthogonal absolute coordinate system having the centerof the CCD camera as the origin is depicted as shown in FIG. 5, thecenters of two spherical waves, that is, the central coordinates of thesingle-mode optical fiber is represented by six unknown quantities ofx1, y1, z1, x2, y2 and z2.

A procedure of obtaining the six unknown quantities is explained below.Before the explanation, parameters of equations to be developed aredefined as follows.

I₀: Light intensity at the center of the CCD camera

A: Amplitude of optical fiber

r₁: Distance from optical fiber to the center of the CCD camera

r₂: Distance from optical fiber to the center of the CCD camera

${\Pi\text{:}\mspace{14mu}\frac{A_{1}^{2}}{r_{1}^{2}}} + \frac{A_{2}^{2}}{r_{2}^{2}}$$\Gamma_{0}\text{:}\mspace{14mu} 2\frac{A_{1}A_{2}}{r_{1}r_{2}}$

Δφ: Initial phase difference of two optical fibers

i, j Pixels deviated from the center of the CCD camera

k: wave number (2π/λ)

{overscore (Λ)}_(ij): Coordinate value according to modeling

Λ_(ij): Coordinate value according to measurement

E: Difference between the measured coordinate value and the modelingcoordinate value

F: Size of one pixel of the CCD camera (=10 μm)

Two spherical waves, which respectively start from the centralcoordinates (x1, y1, z1) of the optical fiber 50 and the centralcoordinates (x2, y2, z2) of the optical fiber 60 in thethree-dimensional space and arrive at the center of the CCD, that is,the origin of the coordinate system, are represented as the followingequations (1) and (2).

$\begin{matrix}{{u_{1} = {\frac{A_{1}}{r_{1}}{\mathbb{e}}^{- {j{({{k\; r_{1}} + \phi_{1}})}}}}},{{{where}\mspace{14mu} r_{1}} = \sqrt{x_{1}^{2} + y_{1}^{2} + z_{1}^{2}}}} & ( {{Equation}\mspace{20mu} 1} ) \\{{u_{2} = {\frac{A_{2}}{r_{2}}{\mathbb{e}}^{- {j{({{k\; r_{2}} + \phi_{2}})}}}}},{{{where}\mspace{14mu} r_{2}} = \sqrt{x_{2}^{2} + y_{2}^{2} + z_{2}^{2}}}} & ( {{Equation}{\;\mspace{11mu}}2} )\end{matrix}$

In the equations 1 and 2, φ₁ and φ₂ respectively mean initial phases ofthe ends of the optical fibers 50 and 60. Accordingly, light intensityobtained from the center of the CCD according to the two spherical wavescan be represented as follows.

$\begin{matrix}\begin{matrix}{I_{0} = {\frac{A_{1}^{2}}{r_{1}^{2}} + \frac{A_{2}^{2}}{r_{2}^{2}} + {2\frac{A_{1}}{r_{1}}\frac{A_{2}}{r_{2}}{\cos\lbrack {{k( {r_{1} - r_{2}} )} + \phi_{1} + \phi_{2}} \rbrack}}}} \\{= {\Pi_{0} + {\Gamma_{0}{\cos\lbrack {{k( {r_{1} - r_{2}} )} + {\Delta\varphi}} \rbrack}}}}\end{matrix} & ( {{Equation}\mspace{20mu} 3} )\end{matrix}$

Since the size of one pixel of the CCD is 10 μm, light intensity at thepoint CCD (i, j) in FIG. 5 can be represented as follows.

$\begin{matrix}{I_{ij} = {\frac{A_{1{ij}}^{2}}{r_{1{ij}}^{2}} + \frac{A_{2{ij}}^{2}}{r_{2{ij}}^{2}} + {2\frac{A_{1{ij}}}{r_{1{ij}}}\frac{A_{2{ij}}}{r_{2{ij}}}{\cos\lbrack {{k( {r_{1{ij}} - r_{2{ij}}} )} + {\Delta\phi}} \rbrack}}}} \\{= {\Pi_{ij} + {\Gamma_{ij}{\cos\lbrack {{k( {r_{1{ij}} - r_{2{if}}} )} + {\Delta\phi}} \rbrack}}}}\end{matrix}$wherer _(1ij)=√{square root over ((x ₁ −i×F ²)+(y ₁ −i×F ²)+z ₁ ²)}{squareroot over ((x ₁ −i×F ²)+(y ₁ −i×F ²)+z ₁ ²)} r _(2ij)=√{square root over((x ₂ −i×F ²)+(y ₂ −i×F ²)+z ₂ ²)}{square root over ((x ₂ −i×F ²)+(y ₂−i×F ²)+z ₂ ²)} F=10 μm  (Equation 4)

When the phase of one of the optical fiber is shifted by δ_(k) in theequation 4 in order to employ a phase-shifting technique, lightintensity is represented as follows.I _(ijk)=Π_(ij)+Γ_(ij) cos [k(r _(1ij) −r _(2ij))+Δφ−δ_(k)]  (Equation5)

If light intensity when the quantity of phase shift, δ_(k), is zero,that is, before the phase shift is made, is represented as I_(ij0),P_(ijk) can be defined as follows.

$\begin{matrix}\begin{matrix}{P_{{ij}\; k} = {I_{{ij}\; k} - I_{ij0}}} \\{= {{\Gamma_{ij}\cos\;{\Phi_{ij}( {{\cos\;\delta_{k}} - 1} )}} + {\Gamma_{ij}\sin\;\Phi_{ij}\sin\;\delta_{k}}}} \\{= {{C_{ij}( {{\cos\;\delta_{k}} - 1} )} + {S_{ij}\sin\;\delta_{k}}}}\end{matrix} & ( {{Equation}\mspace{20mu} 6} )\end{matrix}$where Φ_(ij)=k(r_(1ij)−r_(2ij))+Δφ

When an arbitrary phase shift algorithm is introduced into the equation6, phase Φ_(ij) can be obtained irrespective of the quantity of phaseshift δ_(k).

When the phase Φ_(ij) is acquired in the equation 6, seven unknownquantities x1, y1, z1, x2, y2, z2 and ΔΦ are included therein.Accordingly, from a new phase difference obtained by subtracting phaseΦ₀₀ from the phase Φ_(ij) in the CCD central coordinates (i=0, j=0),Λ_(ij) is defined as follows.

$\begin{matrix}{\Lambda_{ij} = {\frac{\Phi_{ij} - \Phi_{00}}{k} = {r_{1{ij}} - r_{{2{ij}}\;} - r_{100} - r_{200}}}} & ( {{Equation}\mspace{20mu} 7} )\end{matrix}$

As described above, Λ_(ij) is represented by the six unknown quantitiesx1, x1, z1, x2, y2 and z2. Therefore, an object function to be minimizedis defined as follows.

$\begin{matrix}{E = {\sum\limits_{i,j}( {\Lambda_{ij} - \overset{\_}{\Lambda_{ij}}} )^{2}}} & ( {{Equation}\mspace{20mu} 8} )\end{matrix}$

Here, {overscore (Λ)}_(ij) means the measurement value of Λ_(ij), and

$\sum\limits_{i,j}$means that (Λ_(ij)−{overscore (Λ_(ij))})² is summed for CCD pixels.Because the object function defined as above is convex, its convergenceis guaranteed but it is nonlinear for the six unknown quantities.Accordingly, nonlinear optimization is required.

The nonlinear optimization needs two algorithms for determining adirection and a step size, and these two algorithms are repeatedlyexecuted to obtain an optimal position.

The present invention uses the modified Newton's method, which is astable nonlinear optimization with high convergence speed, as thealgorithm for determining a direction. The modified Newton's method hasa fast convergence speed because it quadratic-converges, and it issuitable for solving approximately six unknown quantities. BFGC used inthe present invention is the algorithm whose performance was verified invarious ways and widely being employed in the academic world. Thealgorithm for determining a size includes Armijo method that is fast,Trust region method and quadratic fitting method with high accuracy. Thepresent invention uses the Armijo method in a region near the initialposition and uses the quadratic fitting method in a region close to theoptimal position so as to improve optimization performance, therebymeeting a given problem.

The speed of the optimization algorithm of obtaining the six unknownquantities described above depends on how close the initial position isassumed to be placed to the optimal position. Therefore, the inventionuses the following additional items in order to access the initialposition more systematically.

In the equation 6, Taylor progression of the phase Λ_(ij) is developedfor i and j as follows.

$\begin{matrix}\begin{matrix}{\Lambda_{ij} = {\Lambda_{ij} = {❘_{\underset{j = 0}{i = 0}}{{+ \frac{\partial\Lambda_{ij}}{\partial i}}❘_{\underset{j = 0}{i = 0}}{{i + \frac{\partial\Lambda_{ij}}{\partial j}}❘_{\underset{j = 0}{i = 0}}{j +}}}}}} \\{\frac{\partial^{2}\Lambda_{{ij}\;}}{{{\partial i}\; j}\;}❘_{\underset{j = 0}{i = 0}}{{{i\; j} + {\frac{1}{2}\frac{\partial^{2}\Lambda_{ij}}{\partial i^{2}}}}❘_{\underset{j = 0}{i = 0}}{i^{2} + \cdots}}}\end{matrix} & ( {{Equation}{\mspace{11mu}\;}9} )\end{matrix}$

Meanwhile, when Zernike polynomial is applied to the obtained positive{overscore (Λ)}_(ij), it is represented by the following equation 10.

$\begin{matrix}{\Lambda_{ij} = {\sum\limits_{n}{a_{n}{Z_{n}( {i,j} )}}}} & ( {{Equation}\mspace{20mu} 10} )\end{matrix}$

Here, Z₀=1, Z₁=i, Z₂=j, Z₃=2_(ij), . . .

Where the equations 9 and 10 are compared with each other, Zernikefactors are represented as the following equations 11, 12 and 13 whenthey are given physical meanings.

$\begin{matrix}{{{a_{1} = \frac{\partial\Lambda_{ij}}{\partial i}}}_{\underset{j = 0}{i = 0}} = {\frac{x_{2}}{r_{200}} - \frac{x_{1}}{r_{100}}}} & ( {{Equation}\mspace{20mu} 11} ) \\{{{a_{2} = \frac{\partial\Lambda_{ij}}{\partial j}}}_{\underset{j = 0}{i = 0}} = {\frac{y_{2}}{r_{200}} - \frac{y_{1}}{r_{100}}}} & ( {{Equation}\mspace{20mu} 12} ) \\{{{a_{3} = {\frac{1}{2}\frac{\partial\Lambda_{ij}}{\partial{ij}}}}}_{\underset{j = 0}{i = 0}} = {{\frac{1}{2}\frac{x_{2}y_{2}}{r_{200}^{3}}} - \frac{x_{1}y_{1}}{r_{100}^{3}}}} & ( {{Equation}\mspace{20mu} 13} )\end{matrix}$

The equations 11, 12 and 13 are arranged as follows.

$\begin{matrix}\begin{matrix}{r_{200} = \frac{( {a_{1} + \frac{x_{1}}{r_{100}}} )( {a_{2} + \frac{y_{1}}{r_{100}}} )}{{2a_{3}} + \frac{x_{1}y_{1}}{r_{100}}}} \\{= \frac{( {a_{1} + \frac{x_{1}}{\sqrt{x_{1}^{2} + y_{1}^{2} + z_{1}^{2}}}} )}{{2a_{3}} + \frac{x_{1}y_{1}}{( {x_{1}^{2} + y_{1}^{2} + z_{1}^{2}} )^{3/2}}}} \\{x_{2} = {r_{200}( {a_{1} + \frac{x_{1}}{\sqrt{x_{1}^{2} + y_{1}^{2} + z_{1}^{2}}}} )}} \\{y_{2} = {r_{200}( {a_{1} + \frac{y_{1}}{\sqrt{x_{1}^{2} + y_{1}^{2} + z_{1}^{2}}}} )}}\end{matrix} & ( {{Equation}\mspace{20mu} 14} )\end{matrix}$z ₂ =√{square root over (r ²⁰⁰ ² −x ² ² −y ² ² )}

If the initial positions x1, y1 and z1 are assumed, therefore, x2, y2and z2 can be obtained through the equation 14 from the measured Zernikefactors. Because the initial positions are assumed values, x2, y2 and z2obtained through the equation 14 are also deviated from the optimalposition. However, values closer to the optimal position can beacquired, compared to the case of assuming all of the six unknownquantities, so that it is possible to reach the optimal position with asmall number of times of repetition.

When the nonlinear optimization is performed through a simulation asdescribed above, if an initially set value of less than ±100 μm is givento the six unknown quantities in a hexahedron of 150 nm, convergenceoccurs within the optimal position of 10 nm within 0.98 sec. Accordingto the above-described method, the measurement value ({overscore(Λ)}_(ij)) according to the initial modeling can approximate to theactually measured value (Λ_(ij)) resulting in fast calculation andreduction in errors of measured coordinate values.

FIG. 6 illustrates an embodiment of measuring interference patternsusing at least three CCD cameras in case where the optical fibers areconnected with the probe in the manner shown in FIG. 4 or 4A. Though atleast three CCD cameras can be set for the optical fibers connected withthe probe in the form of FIG. 4, it is preferable to set at least threeCCD cameras for the probe in the form of FIG. 4A, which can generatewider spherical wave. The reason why at least three cameras are set isthat interference patterns can be measured irrespective of the height ofthe object to be measured because spherical wave can be detected fromother sides in case where the object to be measured is higher than theprobe. Furthermore, at least three interference patterns inputted fromat least three CCD cameras are detected and the average curvature ofcurvatures of the detected interference patterns is obtained so thatmore accurate measurement can be made. The procedure of obtaining theaverage curvature includes arithmetic average and so on and explanationtherefore is omitted in the present invention.

FIG. 7 illustrates another system for generating spherical waves. Alateral shearing interferometer (LSI) 200 is a device of generating twospherical waves having different phases. Beam is generated from an innerlight source 201 and passes through a lens 202, a one-pin hole 203 and alens 204, and two waves having different phases are generated from thebeam through a lateral shearing unit 210 and pass through a lens 206 anda two-pin hole 207 having two holes, thereby generating two sphericalwaves. In this procedure, power supplied by the computer 90 controls aPZT 205 inside the LSI 200 to create two spherical waves havingdifferent phases. This is included in the technical fields of prior artsso that detailed explanation for the LSI is omitted. Since two sphericalwaves having different phases can be generated even with theaforementioned technique, interference patterns can be obtained usingthe spherical waves. Furthermore, three-dimensional coordinates of anobject to be measured can be extracted by placing the object under theLSI.

FIG. 8 illustrates another form of the probe that can be used in anarrow space. In case of a small measurement range, that is, tens tohundreds micrometers (for example, STM, AFM and the like), one of theoptical fibers is fixed and measurement is carried out through aninterface pattern generated by moving the other optical fiber in orderto measure and correct three-dimensional coordinates of a moving probe.Specifically, the optical fiber 50 is fixed to a fixed probe 801 and amoving probe 802 is moved to measure the interference pattern with theCCD camera 100 so as to extract coordinate values. Here, the fixed probe801 has a fixed coordinate value so that it can be calculated having r₁or r₂ in the equations 1 and 2 used for extracting coordinate values asan initial value. This simplifies entire equations. Accordingly,extraction of only the coordinate value of the moving probe 802 isrequired, which is allowable when the probe is moved within a narrowspace.

FIG. 9 is a flow chart showing a procedure of measuring athree-dimensional position according to the present invention. In thepresent invention, the three-dimensional position is measured usinginterference patterns measured with voltage generated from a computer,being divided into three steps.

The procedure includes a first step of adjusting a position of theprobe, a second step of judging matching of the position of the probe, athird step of resetting steps of voltage applied to the PZT when theprobe position is matched, a fourth step of adding 1 to the steps of thevoltage applied to the PZT, a fifth step of judging if the steps of thevoltage applied to the PZT exceeds 3, a sixth step of detectinginterference patterns to obtain coordinates and storing the detectedcoordinates in a database, and a seventh step of displaying and storingthree-dimensional coordinates of x1, y1, z1 or x2, y2, z2 when the stepsof the voltage applied to the PZT exceeds 4. When voltages havingdifferent levels are applied to the PZT three times at coordinates of afixed position of the probe to correct the position through generationand detection of interference patterns, more accurate measurement can beaccomplished. Though the voltages are applied to the PZT three times tomeasure the interference patterns in this embodiment, the number ofvoltages having different levels applied to the PZT is usually equal to30-40 in actual measurement experiments. Thus, the steps of theaforementioned procedure can be increased or decreased on the technicallevel of those skilled in the art.

1. A system for determining coordinates in a three-dimensional spaceusing a beam phase interference method, comprising: a light source thatprovides a beam to two optical fibers, a first end of each of said twooptical fibers being set inside a probe, the probe being placed in thethree-dimensional space; a fiber coupler positioned proximate a front ofsaid light source that splits said beam emitted from said light sourceinto two beams, a second end of each of said two optical fibers beingconnected to said fiber coupler, one of said two optical fibers beingconnected with a PZT that changes an optical path; an image capturingunit that acquires an interference pattern generated by beams emittedfrom said two optical fibers set inside the probe; and acontrol/analysis unit that calculates an acquired interference patternto determine a curvature and a central point of the interferencepattern.
 2. A system for determining coordinates in a three-dimensionalspace using a beam phase interference method, comprising: a light sourcethat provides a beam to two optical fibers, a first end of a firstoptical fiber of said two optical fibers being set inside a probe, theprobe being placed in the three-dimensional space, a first end of asecond optical fiber of said two optical fibers being fixed to a fixingmember; a fiber coupler positioned proximate a front of said lightsource that splits a beam emitted from the light source into two beams,a second end of said first optical fiber and a second end of said secondoptical fiber being connected to said fiber coupler, one of said twooptical fibers being connected with a PZT that changes an optical path;an image capturing unit that acquires an interference pattern generatedby beams emitted from the optical fiber set inside the probe and theoptical fiber fixed to the fixing member; and a control/analysis unitthat calculates an acquired interference pattern to determine acurvature and a central point of the interference pattern.
 3. The systemfor determining coordinates in a three-dimensional space using a beamphase interference method as claimed in claim 1, wherein the imagecapturing unit includes a plurality of CCD cameras, and calculatesinterference patterns captured by at least two CCD cameras to obtainsaid curvatures and said central points of the interference pattern. 4.A method for determining coordinates in a three-dimensional space,comprising: generating spherical waves from two point beam sources;forming an interference pattern in response to the spherical wavesinterfering with each other; changing a phase of one of the two pointbeam sources; forming a second interference pattern in response to thepoint beam source whose phase was changed interfering with the otherpoint beam source; obtaining interference patterns having differentinitial phases through a single image capturing unit, the interferencepatterns being formed by repeating the changing of the phase of one ofthe two point beam sources and the forming of the second interferencepattern; obtaining curvatures of the obtained interference patternsusing a phase shift algorithm; obtaining central points from thecurvatures; and determining the obtained central points as coordinatesin the three-dimensional space.
 5. A method for determining coordinatesin a three-dimensional space, comprising: generating spherical wavesfrom two point beam sources; forming an interference pattern in responseto the spherical waves interfering with each other; changing a phase ofone of the two point beam sources; forming another interference patternin response to the point beam source whose phase was changed interferingwith the other point beam source; obtaining interference patterns havingdifferent initial phases through at least two image capturing units, theinterference patterns being formed by repeating the changing of thephase of one of the two beam point sources and the forming of theanother interference pattern; obtaining curvatures of the interferencepatterns obtained through at least two image capturing units using aphase shift algorithm; averaging the curvatures to obtain one curvature;acquiring a central point from the obtained curvature; and determiningthe obtained central point as coordinates in the three-dimensionalspace.
 6. The system for determining coordinates in a three-dimensionalspace using a beam phase interference method as claimed in claim 2,wherein the image capturing unit for acquiring the interference patternincludes a plurality of CCD cameras, and calculates interferencepatterns captured by at least two CCD cameras to obtain curvatures andcentral points of the interference patterns.